Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
2701	Find the Derivative - d/dx	e-e^x+x^e	$e - e^{x} + x^{e}$
2702	Find the Horizontal Tangent Line	x^2+y^2=8x	$x^{2} + y^{2} = 8 x$
2703	Find the Horizontal Tangent Line	x^2+y^2=2x	$x^{2} + y^{2} = 2 x$
2704	Find the Horizontal Tangent Line	y=x^2+1	$y = x^{2} + 1$
2705	Find the Horizontal Tangent Line	y=x^2	$y = x^{2}$
2706	Find Where dy/dx is Equal to Zero	x=tan(y)	$x = \tan (y)$
2707	Find the Absolute Max and Min over the Interval	f(x)=4x^3-34x^2+60x , 0<x<2.5	$f (x) = 4 x^{3} - 34 x^{2} + 60 x$ , $0 < x < 2.5$
2708	Find the Critical Points	f(x)=2x^3-12x^2-72x+2017	$f (x) = 2 x^{3} - 12 x^{2} - 72 x + 2017$
2709	Find the Critical Points	x+4/x	$x + \frac{4}{x}$
2710	Find the Critical Points	sin(x)	$\sin (x)$
2711	Find the Critical Points	y=x/(x^2+1)	$y = \frac{x}{x^{2} + 1}$
2712	Find the Inflection Points	y=x^3-3x^2-105x	$y = x^{3} - 3 x^{2} - 105 x$
2713	Find the Inflection Points	f(x)=x^3-3x	$f (x) = x^{3} - 3 x$
2714	Find the Inflection Points	f(x)=x^4-2x^2+3	$f (x) = x^{4} - 2 x^{2} + 3$
2715	Find the Concavity	f(x)=x/(x^2+1)	$f (x) = \frac{x}{x^{2} + 1}$
2716	Use the Limit Definition to Find the Derivative	e^x	$e^{x}$
2717	Find the Antiderivative	-cos(x)	$- \cos (x)$
2718	Find the Derivative - d/d@VAR	f(x)=3x^4	$f (x) = 3 x^{4}$
2719	Find the Derivative - d/dx	y=(x^6)/(1-x^5)	$y = \frac{x^{6}}{1 - x^{5}}$
2720	Evaluate the Limit	limit as x approaches 0 of (1-cos(x))/(x^2)	$lim_{x \to 0} \frac{1 - \cos (x)}{x^{2}}$
2721	Find the Derivative - d/dx	x/7-7/x	$\frac{x}{7} - \frac{7}{x}$
2722	Find the Derivative - d/du	(u- square root of u)(u+ square root of u)	$(u - \sqrt{u}) (u + \sqrt{u})$
2723	Find the Derivative - d/d@VAR	f(x)=x/(x^2-9)	$f (x) = \frac{x}{x^{2} - 9}$
2724	Evaluate the Summation	sum from i=1 to 7 of 2^(i-1)	$\sum_{i = 1}^{7} 2^{i - 1}$
2725	Evaluate the Summation	sum from i=0 to 4 of 5^i	$\sum_{i = 0}^{4} 5^{i}$
2726	Find the Derivative of the Integral	integral of square root of x natural log of x with respect to x	$\int \sqrt{x} \ln (x) d x$
2727	Evaluate the Integral	integral of x*sin(x) with respect to x	$\int x \cdot \sin (x) d x$
2728	Evaluate the Integral	integral of 5xcos(4x) with respect to x	$\int 5 x \cos (4 x) d x$
2729	Find the Derivative of the Integral	integral of 1/(x natural log of x) with respect to x	$\int \frac{1}{x \ln (x)} d x$
2730	Find the Derivative - d/dx	(5 square root of x)/6	$\frac{5 \sqrt{x}}{6}$
2731	Evaluate	24/(((5)^2+24)^(3/2))	$\frac{24}{{({(5)}^{2} + 24)}^{\frac{3}{2}}}$
2732	Evaluate	(1.999)^4	${(1.999)}^{4}$
2733	Evaluate the Integral	integral from 1 to 7 of x square root of 4x^2+9 with respect to x	$\int_{1}^{7} x \sqrt{4 x^{2} + 9} d x$
2734	Evaluate the Integral	integral of 12x with respect to x	$\int 12 x d x$
2735	Evaluate the Integral	integral of 14x^6 with respect to x	$\int 14 x^{6} d x$
2736	Evaluate the Integral	integral of 14x natural log of 3x with respect to x	$\int 14 x \ln (3 x) d x$
2737	Evaluate the Integral	integral from 2 to 3 of 1/( square root of x)-5 with respect to x	$\int_{2}^{3} \frac{1}{\sqrt{x}} - 5 d x$
2738	Evaluate the Integral	integral from 1 to 4 of 5x^2+ square root of x with respect to x	$\int_{1}^{4} 5 x^{2} + \sqrt{x} d x$
2739	Evaluate the Integral	integral from 1 to 4 of (e^( square root of x))/( square root of x) with respect to x	$\int_{1}^{4} \frac{e^{\sqrt{x}}}{\sqrt{x}} d x$
2740	Evaluate the Integral	integral from 1 to 4 of 1/( square root of t) with respect to t	$\int_{1}^{4} \frac{1}{\sqrt{t}} d t$
2741	Evaluate the Integral	integral from 1 to 3 of 2/x with respect to x	$\int_{1}^{3} \frac{2}{x} d x$
2742	Evaluate the Integral	integral of (x^2)/(x^4-2x^2-8) with respect to x	$\int \frac{x^{2}}{x^{4} - 2 x^{2} - 8} d x$
2743	Evaluate the Integral	integral from -1 to 2 of 9-x^2 with respect to x	$\int_{- 1}^{2} 9 - x^{2} d x$
2744	Evaluate the Integral	integral from -1 to 1 of cube root of t-2 with respect to t	$\int_{- 1}^{1} \sqrt[3]{t} - 2 d t$
2745	Evaluate the Integral	integral from -1 to 1 of x with respect to x	$\int_{- 1}^{1} x d x$
2746	Evaluate the Integral	integral from 0 to 2 of 3x with respect to x	$\int_{0}^{2} 3 x d x$
2747	Evaluate the Integral	integral from 0 to 3 of (3-t) square root of t with respect to t	$\int_{0}^{3} (3 - t) \sqrt{t} d t$
2748	Evaluate the Integral	integral from 0 to 4 of x^3 with respect to x	$\int_{0}^{4} x^{3} d x$
2749	Evaluate the Integral	integral from 0 to 3 of 35e^t with respect to t	$\int_{0}^{3} 35 e^{t} d t$
2750	Evaluate the Integral	integral from 0 to 5 of x square root of 25-x^2 with respect to x	$\int_{0}^{5} x \sqrt{25 - x^{2}} d x$
2751	Evaluate the Integral	integral from 0 to 4 of 4x-x^2 with respect to x	$\int_{0}^{4} 4 x - x^{2} d x$
2752	Evaluate the Integral	integral from 0 to 8 of x^(1/3) square root of x^(4/3)+9 with respect to x	$\int_{0}^{8} x^{\frac{1}{3}} \sqrt{x^{\frac{4}{3}} + 9} d x$
2753	Evaluate the Integral	integral from 0 to 1 of cos(x^2) with respect to x	$\int_{0}^{1} \cos (x^{2}) d x$
2754	Evaluate the Integral	integral from 0 to 1 of 1/(1+x^2) with respect to x	$\int_{0}^{1} \frac{1}{1 + x^{2}} d x$
2755	Evaluate the Integral	integral from 0 to 1 of e^(-4x) with respect to x	$\int_{0}^{1} e^{- 4 x} d x$
2756	Evaluate the Integral	integral from 0 to 1 of e^(-x^2) with respect to x	$\int_{0}^{1} e^{- x^{2}} d x$
2757	Evaluate the Integral	integral from 0 to 1 of x^11(1+x^12)^11 with respect to x	$\int_{0}^{1} x^{11} {(1 + x^{12})}^{11} d x$
2758	Evaluate the Integral	integral from 0 to square root of 11 of (10x)/( square root of x^2+25) with respect to x	$\int_{0}^{\sqrt{11}} \frac{10 x}{\sqrt{x^{2} + 25}} d x$
2759	Evaluate the Integral	integral from 0 to pi/6 of 9sec(x)^2 with respect to x	$\int_{0}^{\frac{π}{6}} 9 \sec^{2} (x) d x$
2760	Evaluate the Integral	integral of x(x-1)^5 with respect to x	$\int x {(x - 1)}^{5} d x$
2761	Evaluate the Integral	integral of x(2x+5)^8 with respect to x	$\int x {(2 x + 5)}^{8} d x$
2762	Evaluate the Integral	integral of x with respect to y	$\int x d y$
2763	Evaluate the Integral	integral of xarcsin(x) with respect to x	$\int x \arcsin (x) d x$
2764	Evaluate the Integral	integral of xarctan(x^2) with respect to x	$\int x \arctan (x^{2}) d x$
2765	Evaluate the Integral	integral of xsin(3x^2) with respect to x	$\int x \sin (3 x^{2}) d x$
2766	Evaluate the Integral	integral of sec(2x) with respect to x	$\int \sec (2 x) d x$
2767	Evaluate the Integral	integral of tan(4x) with respect to x	$\int \tan (4 x) d x$
2768	Evaluate the Integral	integral of sin(3x)cos(2x) with respect to x	$\int \sin (3 x) \cos (2 x) d x$
2769	Evaluate the Integral	integral of sin(2t) with respect to t	$\int \sin (2 t) d t$
2770	Evaluate the Integral	integral of sin(2x)cos(x) with respect to x	$\int \sin (2 x) \cos (x) d x$
2771	Evaluate the Integral	integral from a to b of 5e^(4t) with respect to t	$\int_{a}^{b} 5 e^{4 t} d t$
2772	Evaluate the Integral	integral from a to b of f(x) with respect to x	$\int_{a}^{b} f (x) d x$
2773	Evaluate the Integral	integral of arcsec(x) with respect to x	$\int arcsec (x) d x$
2774	Evaluate the Integral	integral of cot(2x) with respect to x	$\int \cot (2 x) d x$
2775	Evaluate the Integral	integral of csc(2x) with respect to x	$\int \csc (2 x) d x$
2776	Evaluate the Integral	integral from e to e^2 of 1/(x natural log of x) with respect to x	$\int_{e}^{e^{2}} \frac{1}{x \ln (x)} d x$
2777	Evaluate the Integral	integral of 5x^3 with respect to x	$\int 5 x^{3} d x$
2778	Evaluate the Integral	integral of 5xe^(3x) with respect to x	$\int 5 x e^{3 x} d x$
2779	Evaluate the Integral	integral of 5ydy with respect to y	$\int 5 yds y d y$
2780	Evaluate the Integral	integral of 5sec(x)tan(x) with respect to x	$\int 5 \sec (x) \tan (x) d x$
2781	Evaluate the Integral	integral of 9x^-5 with respect to x	$\int 9 x^{- 5} d x$
2782	Evaluate the Integral	integral of 5xcos(2x) with respect to x	$\int 5 x \cos (2 x) d x$
2783	Evaluate the Integral	integral of 7xe^x with respect to x	$\int 7 x e^{x} d x$
2784	Evaluate the Integral	integral of 2x square root of x^2+1 with respect to x	$\int 2 x \sqrt{x^{2} + 1} d x$
2785	Evaluate the Integral	integral from -3 to -2 of 2x(6-x^2)^3 with respect to x	$\int_{- 3}^{- 2} 2 x {(6 - x^{2})}^{3} d x$
2786	Evaluate the Integral	integral of 2xe^(3x) with respect to x	$\int 2 x e^{3 x} d x$
2787	Evaluate the Integral	integral of 2x^2 fourth root of 5+4x^3 with respect to x	$\int 2 x^{2} \sqrt[4]{5 + 4 x^{3}} d x$
2788	Evaluate the Integral	integral of 3 cube root of x^2 with respect to x	$\int 3 \sqrt[3]{x^{2}} d x$
2789	Evaluate the Integral	integral of 3t^2 square root of t^3+2 with respect to t	$\int 3 t^{2} \sqrt{t^{3} + 2} d t$
2790	Evaluate the Integral	integral of xe^(-5x) with respect to x	$\int x e^{- 5 x} d x$
2791	Evaluate the Integral	integral of xe^(3x^2) with respect to x	$\int x e^{3 x^{2}} d x$
2792	Evaluate the Integral	integral from 0 to pi/2 of sin(2x) with respect to x	$\int_{0}^{\frac{π}{2}} \sin (2 x) d x$
2793	Evaluate the Integral	integral from 0 to pi/3 of 5sec(x)^2 with respect to x	$\int_{0}^{\frac{π}{3}} 5 \sec^{2} (x) d x$
2794	Evaluate the Integral	integral of (x+3)/(x^2+6x+7) with respect to x	$\int \frac{x + 3}{x^{2} + 6 x + 7} d x$
2795	Evaluate the Integral	integral of x^3 square root of x^2-1 with respect to x	$\int x^{3} \sqrt{x^{2} - 1} d x$
2796	Evaluate the Integral	integral of square root of 6x with respect to x	$\int \sqrt{6 x} d x$
2797	Evaluate the Integral	integral of square root of 4x+9 with respect to x	$\int \sqrt{4 x + 9} d x$
2798	Evaluate the Integral	integral of square root of 2x-1 with respect to x	$\int \sqrt{2 x - 1} d x$
2799	Evaluate the Integral	integral of square root of 2x-3 with respect to x	$\int \sqrt{2 x - 3} d x$
2800	Evaluate the Integral	integral of (-x)/((x+1)- square root of x+1) with respect to x	$\int \frac{- x}{(x + 1) - \sqrt{x + 1}} d x$